Visit the Pi in the Sky 7 lesson page to explore classroom resources and downloads for the 2019 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

A new Mars landing technique called Range Trigger is reducing the size of the ellipse where spacecraft touch down. Image credit: NASA/JPL-Caltech | › Full image and caption

Composite image of the Kuiper Belt object Arrokoth from NASA's New Horizons spacecraft. Image credit: NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute/Roman Tkachenko | › Full image and caption

The CORAL mission records the spectra of light reflected from the ocean to study the composition and health of Earth's coral reefs. Image credit: NASA | + Expand image

The star Beta Pictoris and its surrounding debris disk in near-infrared light. Image credit: ESO/A.-M. Lagrange et al. | › Full image and caption

Besides providing an excuse to eat all varieties of pie, Pi Day gives us a chance to appreciate some of the ways NASA uses pi to explore the solar system and beyond. You can do the math for yourself – or get students doing it – by taking part in the NASA Pi Day Challenge. Find out below how to test your pi skills with real-world problems faced by NASA space explorers, plus get lessons and resources for educators.

How It Works

The ratio of any circle's circumference to its diameter is equal to pi, which is often rounded to 3.14. But pi is what is known as an irrational number, so its decimal representation never ends, and it never repeats. Though it has been calculated to trillions of digits, we use far fewer at NASA.

Pi is useful for all sorts of things, like calculating the circumference and area of circular objects and the volume of cylinders. That's helpful information for everyone from farmers irrigating crops to tire manufacturers to soup-makers filling their cans. At NASA, we use pi to calculate the densities of planets, point space telescopes at distant stars and galaxies, steer rovers on the Red Planet, put spacecraft into orbit and so much more! With so many practical applications, it's no wonder so many people love pi!

In the U.S., 3.14 is also how we refer to March 14, which is why we celebrate the mathematical marvel that is pi on that date each year. In 2009, the U.S. House of Representatives passed a resolution officially designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi.

The NASA Pi Day Challenge

This year's NASA Pi Day Challenge poses four puzzlers that require pi to compare the sizes of Mars landing areas, calculate the length of a year for one of the most distant objects in the solar system, measure the depth of the ocean from an airplane, and determine the diameter of a distant debris disk. Learn more about the science and engineering behind the problems below or click the link to jump right into the challenge.

› Take the NASA Pi Day Challenge
› Educators, get the lesson here!

Mars Maneuver

Long before a Mars rover touches down on the Red Planet, scientists and engineers must determine where to land. Rather than choosing a specific landing spot, NASA selects an area known as a landing ellipse. A Mars rover could land anywhere within this ellipse. Choosing where the landing ellipse is located requires compromising between getting as close as possible to interesting science targets and avoiding hazards like steep slopes and large boulders, which could quickly bring a mission to its end. In the Mars Maneuver problem, students use pi to see how new technologies have reduced the size of landing ellipses from one Mars rover mission to the next.

Cold Case

In January 2019, NASA's New Horizons spacecraft sped past Arrokoth, a frigid, primitive object that orbits within the Kuiper Belt, a doughnut-shaped ring of icy bodies beyond the orbit of Neptune. Arrokoth is the most distant Kuiper Belt object to be visited by a spacecraft and only the second object in the region to have been explored up close. To get New Horizons to Arrokoth, mission navigators needed to know the orbital properties of the object, such as its speed, distance from the Sun, and the tilt and shape of its orbit. This information is also important for scientists studying the object. In the Cold Case problem, students can use pi to determine how long it takes the distant object to make one trip around the Sun.

Coral Calculus

Coral reefs provide food and shelter to many ocean species and protect coastal communities against extreme weather events. Ocean warming, invasive species, pollutants, and acidification caused by climate change can harm the tiny living coral organisms responsible for building coral reefs. To better understand the health of Earth's coral reefs, NASA's COral Reef Airborne Laboratory, or CORAL, mission maps them from the air using spectroscopy, studying how light interacts with the reefs. To make accurate maps, CORAL must be able to differentiate among coral, algae and sand on the ocean floor from an airplane. And to do that, it needs to calculate the depth of the ocean at every point it maps by measuring how much sunlight passes through the ocean and is reflected upward from the ocean floor. In Coral Calculus, students use pi to measure the water depth of an area mapped by the CORAL mission and help scientists better understand the status of Earth's coral reefs.

Planet Pinpointer

Our galaxy contains billions of stars, many of which are likely home to exoplanets – planets outside our solar system. So how do scientists decide where to look for these worlds? Using data gathered by NASA's Spitzer Space Telescope, researchers found that they're more likely to find giant exoplanets around young stars surrounded by debris disks, which are made up of material similar to what's found in the asteroid belt and Kuiper Belt in our solar system. Sure enough, after discovering a debris disk around the star Beta Pictoris, researchers later confirmed that it is home to at least two giant exoplanets. Learning more about Beta Pictoris' debris disk could give scientists insight into the formation of these giant worlds. In Planet Pinpointer, put yourself in the role of a NASA scientist to learn more about Beta Pictoris' debris disk, using pi to calculate the distance across it.

Participate

• 
  Pi Day Challenge Lessons

  Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

  Grades 4-12

  Time Varies

• 
  Slideshow: NASA Pi Day Challenge

  The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

  Grades 4-12

  Time Varies

• 
  Pi Day: What’s Going ’Round

  Tell us what you’re up to this Pi Day and share your stories and photos with NASA.

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

Blogs and Features

• 
  How Many Decimals of Pi Do We Really Need?

  While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

• 
  Slideshow: 18 Ways NASA Uses Pi

  Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

Related Lessons for Educators

• 
  Rover Lessons

  Explore a collection of standards-aligned STEM lessons all about rovers.

  Grades K-12

  Time Varies

• 
  Touchdown

  Students design and build a shock-absorbing system that will protect two "astronauts" when they land.

  Grades 3-8

  Time 30 mins - 1 hr

• 
  On Target

  Students modify a paper cup so it can zip down a line and drop a marble onto a target.

  Grades 6-12

  Time 30 mins - 1 hr

• 
  Solar System Scale Models

  Explore a collection of standards-aligned STEM lessons all about the size and scale of our solar system.

  Grades 1-12

  Time Varies

• 
  Modeling an Asteroid

  Lead a discussion about asteroids and their physical properties, then have students mold their own asteroids out of clay.

  Grades 3-5

  Time 30 mins - 1 hr

• 
  Math Rocks: A Lesson in Asteroid Dynamics

  Students use math to investigate a real-life asteroid impact.

  Grades 8-12

  Time 30 mins - 1 hr

• 
  Asteroid Ace: A 'Pi in the Sky' Math Challenge

  Students use pi to calculate the rotation rate of an asteroid from another solar system in this illustrated math problem.

  Grades 11-12

  Time < 30 mins

• 
  Climate Change Lessons

  Explore a collection of standards-aligned STEM lessons all about Earth's changing climate.

  Grades K-12

  Time Varies

• 
  Using Light to Study Planets

  Students build a spectrometer using basic materials as a model for how NASA uses spectroscopy to determine the nature of elements found on Earth and other planets.

  Grades 6-11

  Time < 2 hrs

NOAA Coral Bleaching activity

• 
  Solar Sleuth: A 'Pi in the Sky' Math Challenge

  In this illustrated math problem, students use pi and data from the Kepler space telescope to find the size of a planet outside our solar system.

  Grades 6-9

  Time < 30 mins

• 
  Exploring Exoplanets with Kepler

  Students use math concepts related to transits to discover real-world data about Mercury, Venus and planets outside our solar system.

  Grades 6-12

  Time 30 mins - 1 hr

• 
  Habitable Hunt: A 'Pi in the Sky' Math Challenge

  In this illustrated math problem, students use the mathematical constant pi to find the "habitable zone" around a distant star and determine which of its planets are in that zone.

  Grades 11-12

  Time < 30 mins

Related Activities for Students

• 
  Make a Moon or Mars Rover Game

  Create a Moon or Mars exploration game using Scratch, a visual programming language. Think like NASA space-mission planners to design your game!

  Type Project

  Subject Technology

• 
  Make a Cardboard Rover

  Build a rubber-band-powered rover that can scramble across a room.

  Type Project

  Subject Engineering

• 
  Mars in a Minute: How Do You Choose a Landing Site?

  So, you want to study Mars with a lander or rover – but where exactly do you send it? Learn how scientists and engineers tackle the question of where to land on Mars in this 60-second video.

  Type Video

  Subject Engineering

• 
  Mars in a Minute: How Do You Land on Mars?

  Getting a spacecraft to Mars is one thing. Getting it safely to the ground is a whole other challenge! This 60-second video from NASA's Jet Propulsion Laboratory explains three ways to land on the surface of the Red Planet.

  Type Video

  Subject Engineering

• 
  What's That Space Rock?

  Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.

  Type Slideshow

  Subject Science

• 
  Mars in a Minute: How Long is a Year on Mars?

  How long is does it take Mars to make one trip around the Sun and why is one Earth year shorter? Find out in one minute!

  Type Video

  Subject Science

• 
  Space Place in a Snap: The Solar System's Formation

  Find out how our solar system formed and how it came to be the busy place it is today.

  Type Video

  Subject Science

• 
  What Is the Kuiper Belt?

  Learn about the Kuiper Belt and some of its famous members, Kuiper Belt Objects.

  Type Article

  Subject Science

• 
  Coral Bleaching Simulator

  Adjust water temperature and pollution levels in this simulator to see what happens to a coral reef depending on the conditions you choose!

  Type Interactive

  Subject Science

• 
  Ocean Worlds

  Where might oceans – and living things – exist beyond Earth? Scientists have their eyes on these places in our own solar system.

  Type Slideshow

  Subject Science

• 
  NASA's Earth Minute: Mission to Earth?

  NASA doesn't just explore outer space! It studies Earth, too, with a fleet of spacecraft and scientists far and wide.

  Type Video

  Subject Science

• 
  NASA's Earth Minute: Earth Has a Fever

  Why is Earth getting hotter and what does that mean for us?

  Type Video

  Subject Science

NOAA Video Series: Coral Comeback

• Article: Giant Exoplanet Hunters: Look for Debris Disks
• Video: The Evolution of a Planet-Forming Disk
• Video: Birth of "Phoenix" Planets?

Multimedia

• 
  Infographic: Planet Pi

  This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

• Posters: Exoplanet Travel Bureau

Facts and Figures

• Mars
• Arrokoth (2014 MU69)
• Earth
• Beta Pictoris b
• Beta Pictoris c

Missions and Instruments

• Perseverance Mars rover (Mars 2020)
• Curiosity Mars rover
• New Horizons
• CORAL
• Spitzer

Websites

• NASA Mars Exploration
• NASA Solar System Exploration
• NASA Climate Change
• NASA Exoplanets

TAGS: K-12 Education, Math, Pi Day, Pi, NASA Pi Day Challenge, Events, Space, Educators, Teachers, Parents, Students, STEM, Lessons, Problem Set, Mars 2020, Perseverance, Curiosity, Mars rovers, Mars landing, MU69, Arrokoth, New Horizons, Earth science, Climate change, CORAL, NASA Expeditions, coral reefs, oceans, Spitzer, exoplanets, Beta Pictoris, stars, universe, space telescope

• 

  ABOUT THE AUTHOR

  Lyle Tavernier, Educational Technology Specialist, NASA/JPL Edu

  Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.

How It Worked

Human eyes can see only the portion of the electromagnetic spectrum known as visible light. This is because the human retina can detect only certain wavelengths of light through special photoreceptors called rods and cones. Everything we see with our eyes either emits or reflects visible light. But visible light is just a small portion of the electromagnetic spectrum. To "see" things that emit or reflect other wavelengths of light, we must rely on technology designed to sense those portions of the electromagnetic spectrum. Using this specialized technology allows us to peer into space and observe objects and processes we wouldn’t otherwise be able to see.

This diagram shows wavelengths of light on the electromagnetic spectrum and how they're used for various applications. Image credit: NASA | + Expand image

Infrared is one of the wavelengths of light that cannot be seen by human eyes. (It can sometimes be felt by our skin as heat if we are close enough to a strong source.) All objects that have temperature emit many wavelengths of light. The warmer they are, the more light they emit. Most things in the universe are warm enough to emit infrared radiation, and that light can be seen by an infrared-detecting telescope. Because Earth’s atmosphere absorbs most infrared radiation, infrared observations of space are best conducted from outside the planet's atmosphere.

So, to get a look at space objects that were otherwise hidden from view, NASA launched the Spitzer Space Telescope in 2003. Cooled by liquid helium and capable of viewing the sky in infrared, Spitzer launched into an Earth-trailing orbit around the Sun, where it became part of the agency's Great Observatory program along with the visible-light and near-infrared-detecting Hubble Space Telescope, Compton Gamma-Ray Observatory and Chandra X-ray Observatory. (Keeping the telescope cold reduces the chances of heat, or infrared light, from the spacecraft interfering with its astronomical observations.)

Over its lifetime, Spitzer has been used to detect light from objects and regions in space where the human eye and optical, or visible-light-sensing, telescopes may see nothing.

Why It's Important

NASA's Spitzer Space Telescope has returned volumes of data, yielding numerous scientific discoveries.

Vast, dense clouds of dust and gas block our view of many regions of the universe. Infrared light can penetrate these clouds, enabling Spitzer to peer into otherwise hidden regions of star formation, newly forming planetary systems and the centers of galaxies.

The bow shock, or shock wave, in front of the giant star Zeta Ophiuchi shown in this image from Spitzer is visible only in infrared light. The bow shock is created by winds that flow from the star, making ripples in the surrounding dust. Image credit: NASA/JPL-Caltech | › Full image and caption

Infrared astronomy also reveals information about cooler objects in space, such as smaller stars too dim to be detected by their visible light, planets beyond our solar system (called exoplanets) and giant molecular clouds where new stars are born. Additionally, many molecules in space, including organic molecules thought to be key to life's formation, have unique spectral signatures in the infrared. Spitzer has been able to detect those molecules when other instruments have not.

Both NASA's Spitzer and Hubble space telescopes contributed to this vibrant image of the Orion nebula. Spitzer's infrared view exposed carbon-rich molecules, shown in this image as wisps of red and orange. Image credit: NASA/JPL-Caltech/T. Megeath (University of Toledo) & M. Robberto (STScI) | › Full image and caption

Stars are born from condensing clouds of dust and gas. These newly formed stars are optically visible only once they have blown away the cocoon of dust and gas in which they were born. But Spitzer has been able to see infant stars as they form within their gas and dust clouds, helping us learn more about the life cycles of stars and the formation of solar systems.

Newborn stars peek out from beneath their natal blanket of dust in this dynamic image of the Rho Ophiuchi dark cloud from Spitzer. The colors in this image reflect the relative temperatures and evolutionary states of the various stars. The youngest stars are shown as red while more evolved stars are shown as blue. Image credit: NASA/JPL-Caltech/Harvard-Smithsonian CfA | › Full image and caption

Infrared emissions from most galaxies come primarily from stars as well as interstellar gas and dust. With Spitzer, astronomers have been able to see which galaxies are furiously forming stars, locate the regions within them where stars are born and pinpoint the cause of the stellar baby boom. Spitzer has given astronomers valuable insights into the structure of our own Milky Way galaxy by revealing where all the new stars are forming.

This Spitzer image, which covers a horizontal span of 890 light-years, shows hundreds of thousands of stars crowded into the swirling core of our spiral Milky Way galaxy. In visible-light pictures, this region cannot be seen at all because dust lying between Earth and the galactic center blocks our view. Image credit: NASA/JPL-Caltech | › Full image and caption

Spitzer marked a new age in the study of planets outside our solar system by being the first telescope to directly detect light emitted by these so-called exoplanets. This has made it possible for us to directly study and compare these exoplanets. Using Spitzer, astronomers have been able to measure temperatures, winds and the atmospheric composition of exoplanets – and to better understand their potential habitability. The discoveries have even inspired artists at NASA to envision what it might be like to visit these planets.

Thanks to Spitzer, scientists are learning more and more about planets beyond our solar system. These discoveries have even inspired a series of posters created by artists at NASA, who imagined what future explorers might encounter on these faraway worlds. Image credit: NASA/JPL-Caltech | › Download posters

Data collected by Spitzer will continue to be analyzed for decades to come and is sure to yield even more scientific findings. It's certainly not the end of NASA's quest to get an infrared window into our stellar surroundings. In the coming years, the agency plans to launch its James Webb Space Telescope, with a mirror more than seven times the diameter of Spitzer's, to see the universe in even more detail. And NASA's Wide Field Infrared Survey Telescope, or WFIRST, will continue infrared observations in space with improved technology. Stay tuned for even more exciting infrared imagery, discoveries and learning!

Teach It

Use these lessons, videos and online interactive features to teach students how we use various wavelengths of light, including infrared, to learn about our universe:

• 
  Using Light to Study Planets

  Students build a spectrometer using basic materials as a model for how NASA uses spectroscopy to determine the nature of elements found on Earth and other planets.

  Grades 6-11

  Time > 2 hrs

• Lessons: Cool Cosmos Infrared Lessons
• Website: Cool Cosmos Infrared Primer
• Materials: Infrared Posters and Printouts

Explore More

• Article: NASA Celebrates the Legacy of the Spitzer Space Telescope
• Website: Spitzer Space Telescope Mission
• Video: Spitzer Final Voyage VR 360
• Video: Science in a Minute: The Art of Spitzer Space Telescope
• Images: Spitzer Zoomable Images
• Participate: NASA/IPAC Teacher Archive Research Program

Also, check out these related resources for kids from NASA’s Space Place:

• Infrared games, articles and activities

TAGS: Teachable Moments, science, astronomy, K-12 education, teachers, educators, parents, STEM, lessons, activities, Spitzer, Space Telescope, Missions, Spacecraft, Stars, Galaxies, Universe, Infrared, Wavelengths, Spectrum, Light

• 

  ABOUT THE AUTHOR

  Ota Lutz, STEM Elementary and Secondary Education Specialist, NASA/JPL Edu

  Ota Lutz is a STEM elementary and secondary education specialist at NASA’s Jet Propulsion Laboratory. When she’s not writing new lessons or teaching, she’s probably cooking something delicious, volunteering in the community, or dreaming about where she will travel next.

Why It’s Important

These images of Jupiter, Saturn, Uranus and Neptune (clockwise from top) were taken by Voyager 1 and 2 as the spacecraft journeyed through the solar system. See a gallery of images that Voyager took on the Voyager website. Credit: NASA/JPL-Caltech

In addition to shaping our understanding of the outer planets, the Voyager spacecraft are helping us learn more about the space beyond the planets – the outer region of our solar system. After completing their “grand tour” of the outer planets, the Voyagers continued on an extended mission to the outer solar system. They are now more than 10 billion miles from Earth, exploring the boundary region between our planetary system and what’s called interstellar space.

The beginning of interstellar space is where the constant flow of material from the Sun and its magnetic field stop influencing the surroundings. Most of the Sun’s influence is contained within the heliosphere, a bubble created by the Sun and limited by forces in interstellar space. (Note that the heliosphere doesn’t actually look like a sphere when it travels through space; it’s more of a blunt sphere with a tail.) The outer edge of the heliosphere, before interstellar space, is a boundary region called the heliopause. The heliopause is the outermost boundary of the solar wind, a stream of electrically charged atoms, composed primarily of ionized hydrogen, that stream outward from the Sun. Our planetary system lies inside the bubble of the heliosphere, bordered by the heliopause and surrounded by interstellar space.

Though we’ve learned a lot about the heliopause thanks to the Voyager spacecraft, its thickness and variation are still key unanswered questions in space physics. As the Voyagers continue their journey, scientists hope to learn more about the location and properties of the heliopause.

From their unique vantage points – Voyager 1 in the northern hemisphere and Voyager 2 in the southern hemisphere – the spacecraft have already detected differences and asymmetries in the solar wind termination shock, where the wind abruptly slows as it approaches the heliopause. For example, Voyager 2 crossed the termination shock at a distance of about 83.7 AU in the southern hemisphere. (One AU, or astronomical unit, is equal to 150 kilometers (93 million miles), the distance between Earth and the Sun.) That’s about 10 AU closer to the Sun than where Voyager 1 crossed the shock in the north. As shown in this diagram, Voyager 1 traveled through the compressed “nose” of the termination shock and Voyager 2 is expected to travel through the flank of the termination shock.

With four remaining powered instruments on Voyager 1 and five remaining powered instruments on Voyager 2, the two spacecraft continue to collect science data comparing their two distinct locations at the far reaches of the solar system.

In August 2012, Voyager 1 detected a dramatic increase in galactic cosmic rays (as shown in this animated chart). The increase, which has continued to the current peak, was associated with the spacecraft's crossing into interstellar space. Credit: NASA/JPL-Caltech

Since it launched from Earth in 1977, Voyager 1 has been using an instrument to measure high-energy, dangerous particles traveling through space called galactic cosmic rays. While studying the interaction between the bubble of the heliosphere and interstellar space, Voyager 1 revealed that the heliosphere is functioning as a radiation shield, protecting our planetary system from most of these galactic cosmic rays. So in August 2012, when Voyager 1 detected a dramatic increase in the rays, which has continued to the current peak, it was associated with the spacecraft’s crossing into interstellar space.

Meanwhile, Voyager 2 ­­– which is still in the heliosheath, the outermost layer of the heliosphere between the shock and the heliopause ­– is using its solar wind instrument to measure the directional change of solar wind particles there. Within the next few years, Voyager 2 is also expected to cross into interstellar space, providing us with even more detailed data about this mysterious region.

In another 10 years, we expect one or both Voyagers to cruise outward into a more pristine region of interstellar space, returning data to inform our hypotheses about the concentration of galactic particles and the characteristics of interstellar wind.

Even with 40 years of space flight behind them, the Voyagers are expected to continue returning valuable data until about 2025. Communications will be maintained until the spacecraft’s nuclear power sources can no longer supply enough electrical energy to power critical functions. Until then, there’s still much to learn about the boundary of our heliosphere and what lies beyond in the space between the stars.

Teach It

Use these standards-aligned lessons and related activities to get students doing math and science with a real-world (and space!) connection.

• Hear Here - Students use the mathematical constant pi and information about the current location of Voyager 1 to learn about the faint data-filled signal being returned to Earth.
• Solar System Bead Activity – Students calculate and construct a scale model of solar system distances using beads and string.
• Catching a Whisper from Space – Students kinesthetically model the mathematics of how NASA communicates with spacecraft.

Explore More

• Voyager Mission
• Voyager Images
• Voyager Golden Record
• The Sounds of Interstellar Space
• Voyager Senses Sun's Tsunami Wave in Interstellar Medium
• Commemorative Voyager Posters

TAGS: Voyager, Farthest, Golden Record, STEM, Teachable Moments, Science, Engineering, Solar System, Interstellar Space, Heliopause, Heliosphere, Heliosheath, Termination Shock, Stars, Heliophysics

• 

  ABOUT THE AUTHOR

  Ota Lutz, STEM Elementary and Secondary Education Specialist, NASA/JPL Edu

  Ota Lutz is a STEM elementary and secondary education specialist at NASA’s Jet Propulsion Laboratory. When she’s not writing new lessons or teaching, she’s probably cooking something delicious, volunteering in the community, or dreaming about where she will travel next.